# In triangle CDE EC = 26 cm, segment MN is parallel to CE, M belongs to CD, N belongs

In triangle CDE EC = 26 cm, segment MN is parallel to CE, M belongs to CD, N belongs to ED. Find CD if CM = 8 cm, MN = 20 cm.

Let us prove that the triangles CDE and MDN are similar.

In triangles, the angle at the vertex D is common, and the angles DCE and DMN are equal, as are the corresponding angles, at the intersection of the secant CD parallel to CE and MN. Then the triangles CDE and MDN are similar in the first sign of similarity.

Let the segment DМ = X cm, then СD = (X + 8).

EC / NM = DC / DM.

26/20 = (X + 8) / X.

20 * X + 160 = 26 * X.

6 * X = 160.

X = 160/6 = 80/3.

Then SD = 80/3 + 8 = 104/3 = 34 (2/3) cm.

Answer: SD = 34 (2/3) cm. One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.